Let X = (X1, X, )" be a bivariate random variable with variance-covariance matrix4-1.5E(X – E(X))(X – E(X))") = (-1.51You are given thatX1 + aX2is independent of X1.Find the number a. Give your answer in 2 decimal places.Answer:

Answered: Image /qna-images/answer/df6d88be-740f-4aea-a251-7dd69f1a754c.jpg

Answered: Find the number a. Give your answer in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let X1, X2 be two independent random variables with the same mean EXi = µ andpossibly different variances Var(Xi) = σ2i (sigma squared i), i = 1, 2. Consider the weighted average Y =λX1 + (1 − λ)X2 where λ is a constant.(a) Compute EY and Var(Y )(b) Find the λ in terms of σ2i (sigma squared i) , i = 1, 2 that minimizes Var(Y ).
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Suppose X has a trivariate normal distribution with mean vector 0 and covariance matrix 1 0.5 0.25 0.5 1 0 0.25 0 1 A. Find the joint distribution of W1 = X1+X2+X3 and W2 = X1 - X3 B. Find the joint distribution of (X1, X2) GIVEN X3=X3 C. P(max(X1,X2)<X3) D. P(X1>X2|X3=1)
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Suppose Xn is an IID Gaussian process, withµX[n]=1, and σ2 X[n]=1Now, another stochastic process Yn = Xn − Xn−1. Please find:(a) The mean µY (n).(b) The variance σ2Y (n).(c) The auto-correlation RY (n, k)

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